Adventures | Photography of Jeff Ambrose

Paragliding-The Energy Equation

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Several months ago I wrote an article about Managing The Risks of paragliding, which spurred a lot of great conversations and comments. Reflecting on that article, one of the items I mentioned was to make sure we understand which side of the energy equation we are flying on. Several pilots asked great follow up questions wondering what that meant, and how best to apply it. Therefore, in the spirit of sharing, I thought I would discuss my approach to the energy equation and how it works for me.

Let’s talk ENERGY – It is everywhere, it is in everything, and it is a critical concept not only in paragliding, but in ALL types of aviation. Learning to manage energy is one of the fundamental principles every pilot should learn. I say should learn because I do not think many paragliding schools teach it, so it’s up to you! Energy can be boiled down to basically two kinds, Potential Energy (PE) and Kinetic Energy (KE). Understanding how to balance both is vital to safely flying a paraglider. Today we are going to focus on a portion of Kinetic Energy, or more precisely the moving energy of the air over and around our wing.

What we are really trying to determine with this whole energy discussion, is deciding at any given time what has the energy advantage. Is it the glider, or is it the surrounding air? Let me ask it in a more practical way. On any given flight, if you had to quickly get on the ground, out of this canyon, out of this thermal, or even just get out in front of the ridge….could you? If your answer is yes, then your wing has the energy advantage, and that is what we consider being on the right side of the energy equation. I think we have all had times when we realized the air had the advantage and thus we were on the wrong side. It is scary getting blown backwards over a ridge, or going up at 3000 feet/min in a violent thermal, or being sucked into a canyon…well, it is for me at least. I find it is best to eliminate those scenarios before I decide to fly, and the best way is to survey the energy!

For a little more of a scientific approach, the following is an energy equation I developed that helps me make informed decisions. I do not claim it to be right for everybody, but it works for me. I fly primarily the rougher mountains, and am often alone, so a systematic approach has helped me be less emotional and more calculated in my decisions. The equation is simply:

[Glider Energy] – [Air Energy]
which seems to make sense in that who has the advantage, the glider or the surrounding air?

[Glider Energy] (mph) = Airspeed, which is the actual speed of the air traveling over your wing to keep it flying. This is usually the trim speed of your glider, but can vary depending on how slow or fast you decide to fly. Once you get comfortable using the equation it can help you see why we want to fly faster in turbulent air, and why so often your speed system actually helps stabilize your wing in rough conditions.

[Air Energy] (mph) is a little more difficult to determine as it is the amount of swirling air around you which can possibly disrupt or counteract your airspeed. When airspeed is disrupted too much, you get a collapse. In order to determine the Air Energy, we need to break this out a bit:

[Air Energy] = [Wind]*[Terrain Factor] + [Gust]

[Wind] (mph) is the Base wind you feel sitting on launch (or what you measure while flying).

[Terrain Factor] is a unitless number from 0.0 to 1.0 that measures the roughness of the terrain (0.0 meaning completely featureless and smooth while 1.0 is the roughest mountain terrain possible). Most ridge soaring sites are 0.0-0.4, while most mountain sites are 0.5-1.0. The purpose of a terrain factor has everything to do with how wind and thermals interact with the terrain. In rough terrain it is possible to have the base wind actually reverse back on you in small localized gusts. These can be as small as your wing and only last a couple of seconds. These small gusts can disrupt the airflow over your wing thus causing potential collapses. In rough terrain this happens more often, with more force, hence the higher terrain factor.

[Gust] (mph) is the amount of thermal energy you feel while on the ground. This is the gust on top of the base wind that you feel. This thermal energy is from spinning air (thermals are not columns of air going up, they are columns of spinning air with a vertical component). This spinning air can go both ways, and if the spinning air is strong enough it can blow back against the wing, disrupting air flow and thus cause a collapse.

This is the type of site that would have a terrain factor approaching 1.0

I know this is starting to feel like actual math here, but it is pretty easy and quick, with no pocket protector nor calculator required. Let’s look at a few situations that help put it into action:

Example 1: While sitting on the ground, feeling the steady breeze mixed with thermals rolling up the hill, it is tempting to clip in and go, but should you? You are at your home site, a fairly technical mountain launch with a terrain factor of 0.8. The base wind is about 10 mph blowing straight in. Occasionally you feel about an 8 mph gust on top of the base wind. You fly your glider with an airspeed of about 25 mph, and the stall speed of your glider is about 15 mph. Let’s do the quick math.

Therefore, 25 mph – 16 mph = 9 mph. This is the potential worst case airspeed you can expect going over your wing. Is it MORE than the required 15 mph stall speed of your glider? NO! That means you can be sure that the air has the energy advantage in this situation, not your glider. Therefore you can likely expect collapses and other less fun things to happen. Best to stay on the ground for this one.

Example 2: The next day you try again. You hike up to the same technical mountain site with a terrain factor of 0.8. The base wind is 5 mph straight in with a gust of about 5 mph (means the wind goes from 5 mph to 10 mph at the peak). Feels pretty good, should you fly? Let’s do the quick math.

Therefore, 25 mph – 9 mph = 16 mph. This is the potential worst case airspeed going over your wing. Is it MORE than the required 15 mph stall speed of your glider? YES! that means you can be sure that your glider has the energy advantage in this situation, not the air. Therefore you can likely expect little to no collapses and a fun, relatively mellow flight. Time to get in the air.

This simple mathematical approach is what I have used through the years when trying to assess a flying site. No, it is not perfect, but it has helped me put aside emotion and make better decisions inline with my personal risk tolerance. Hopefully you find this discussion helpful in your flying pursuits. I would encourage each of you to find your own approach to energy and make a conscious effort to fly on the right side of the equation. Wishing you all safe and happy flying, and I hope to see you up high in the mountain air soon.

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7 Comments

To me, you mostly talk about relative wind speed, and you are very right that we always want the relative wind speed to be above our stall speed, and your wind-speed equation taking into account the roughness of the terrain is spot on.

However, there is more to be learned about the permanent exchange between potential energy and kinetic energy:

1- Kinetic energy is the energy of our body+ glider relative to our actual speed (not our air speed). It is equal to ½*M*V**2 where M is our mass (say in kilograms, I am trained in European metric system) and V is our speed in meter/s. So if our wing speed is 36km/h (about 20mph) in calm air our speed is 10m/s and our kinetic energy is 50*M in joules and M in kilograms.

2- Potential energy (to be more precise gravitational potential energy) is the energy we gain by fighting against gravity and going higher. It is simply M*H*g where g is the 9.81m/s**2 constant of gravity (not the same on the moon) and H is the height we have gained in meters.

Why does it all matter? Because as we fly we are constantly exchanging kinetic energy and potential energy. So let us do the simplest computation: if we are flying at 10m/s against a wind of 10m/s, that is we are just stuck against the wind (which happens a lot whenever we soar and which happens when we land), and all of a sudden the wind drops to 0 (either turbulence or wind gradient), what is the minimum altitude we must lose before we regain or speed of 10m/s: simple M*H*g = ½ * M * v**2, we remove M from the equation, and we get 9,81H = 50 so H = 5m, that is 15ft.

This means that we can crash from 15ft on landing if we have a really bad wind gradient and we do not try to fly as fast as possible as we approach, or that we need at least 15ft of clearance to “accommodate” a gust of 20mph as we are flying against the wind.

Now because the energy transformation is not perfect, because of the pendulum effect of the wing, because it may not recover as smoothly as we wish, etc… I would assume that we need at least double that to be safe, that is 30ft. This is a very high altitude to fall from, and this indeed shows we should always stay on the right side of the energy curve, that is high enough to clear a wind fluctuation which would force us to exchange our potential energy for the minimum kinetic energy to avoid stalling.

So let us combine this and your wind fluctuation equations, and we have two good curves to keep in mind to fly safe.

Yes! This is exactly how we’re suppose to be thinking as pilots! Well said Pierre.
You are talking mostly about the never ending balancing act between PE and KE. One we must always be doing while flying. Everything we do in a paraglider creates a transfer of energy. Throwing your reserve requires you to spend valuable PE in order to achieve the KE required to open the chute. What happens if you don’t have enough PE stored to do it?….well you hit the ground and die, or break yourself. That is what I call being in the red zone (not enough PE to complete a KE task). Everything is this way and we must always balance it. My article was not really discussing this energy balance, just a quick way to make sure that when flying through those red zones, your likelihood of not getting a collapse is much greater. You are correct in that there are several other energy curves we need to be balancing at all times.
Love your thoughts Pierre, and thanks for showing us that paragliding is actually an intellectual exercise, not just a fun rollercoaster ride.

Jeff, another idea as I was pondering your permanent exchange of PE vs KE.

You know why hot air rises (and takes us paragliders up)? Again, a PE/KE exchange. Never thought about it.

“Hot” air is in fact air with gas particles that are moving faster than the surrounding particles, that is they have more kinetic energy. And what do they do? They exchange this extra speed for extra height, thus rising and transforming their kinetic energy into potential energy until they reach a layer which is “at the same temperature” or “at the same speed”. Or they (the gas particles) bounce on the intrados of a paraglider and provide our much needed lift.

I had never thought of it like that, see how interesting your idea was!

BTW, this also explains the “inversion” issue, where “slow”(=”cold”) air meets a “faster”(=”warmer”) air and can no longer rise, thus trapping all the other particles in the smog we sometimes experience in this season. I love science 😉

Matt-thanks for the math check. The example should have said a base wind of 5 and a gust of 5 (meaning the wind went from 5mph to 10mph at the peak). I have modified the example to the correct numbers, so hopefully that makes more sense.